Abstract
In this paper we discuss the numerical computation of solutions of the nonlinear, two parameter, problem
where x ∈ R n is a State variable, λ and α are parameters, and f is a smooth function. Many physical systems can be described by equations like (1.1), see for example, [l],[3],[l2] and [7],[17], where there are more than two parameters.
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References
Bazley,N.W. and Wake, G.C. The disappearance of criticality in the theory of thermal ignition. ZAMP, 29, (1979), p. 971–976.
Chan, T.F., On the existence and computation of LU-factorizations with small pivots (to appear in Maths. Comp.).
Cliffe, K.A., Numerical calculations of two-cell and Single cell Taylor flows. (To appear in J. Fluid Mech.).
Cliffe, K.A. and Spence, A., The Calculation of High Order Singularities in the Taylor Problem (this proceedings).
Dennis, J.E. and More, J.J., (1977) Quasi-Newton methods, motivation and theory. SIAM Rev. 19, 46–89.
Golub, G.H. and Wilkinson, J.H., (1976) Ill-conditioned eigensystems and the computation of the Jordan canonical form. SIAM Rev. 18, p. 578–619.
Heinemann, R.F. and Poore, A.B., (1981) Multiplicity, Stability and Oscillatory Dynamics of the Tubulär Reactor, Chem. Eng. Sei. 36, pp. 1411–1419.
Jepson, A. and Spence, A., (1982) Folds in solutions of two para-meter systems and their calculation: Part I. Stanford University Technical Report, (submitted to SIAM JNA).
Jepson, A. and Spence, A.f Paths of Singular Points and their Computation (this proceedings).
Jepson A. and Spence, A., (1983) The numerical Solution of non-linear equations having several parameters,Part I: Scalar Equations. (submitted).
Keller, H.B., Singular Systems, Inverse Iterations and least squares (private communication).
Keller, H.B. and Szeto, R.K-H., (1980) Calculation of flows between rotating disks, in “Computing Methods in Applied Sciences and Engineering” ed. R. Glowinski and J.L. Lions, North Holland, p. 51–61.
Melhem, R.G. and Rheinboldt, W.C. (1982) A comparison of methods for determining turning points of nonlinear equations, Computing, 29, p. 201–226.
Rheinboldt, W.G. and Burkardt, J.V., (1983) “A locally parameterized continuation process”, ACM TOMS, 9, p. 215–235.
Spence, A. and Werner, B. (1982) Nonsimple turning points and cusps, IMA J. of Numer. Anal. 2, p.413–427.
Uppal, A., Ray, W.H. and Poore of continuously stirred tank reactors, Chem. Eng. Sei., 29, p. 967–985.
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Spence, A., Jepson, A.D. (1984). The Numerical Calculation of Cusps, Bifurcation Points and Isola Formation Points in Two Parameter Problems. In: Küpper, T., Mittelmann, H.D., Weber, H. (eds) Numerical Methods for Bifurcation Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6256-1_35
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DOI: https://doi.org/10.1007/978-3-0348-6256-1_35
Publisher Name: Birkhäuser, Basel
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